746
REVIEW AND SUMMARY
This chapter was devoted to Newton’s second law and its application
to the analysis of the motion of particles.
Denoting by
m
the mass of a particle, by
o
F
the sum, or resultant,
of the forces acting on the particle, and by
a
the acceleration of the
particle relative to a
newtonian frame of reference
[Sec. 12.2], we
wrote
o
F
5
m
a
(12.2)
Introducing the
linear momentum
of a particle,
L
5
m
v
[Sec. 12.3],
we saw that Newton’s second law can also be written in the form
o
F
5
L
˙
(12.5)
which expresses that
the resultant of the forces acting on a particle is
equal to the rate of change of the linear momentum of the particle
.
Equation (12.2) holds only if a consistent system of units is used. With
SI units, the forces should be expressed in newtons, the masses in
kilograms, and the accelerations in m/s
2
; with U.S. customary units,
the forces should be expressed in pounds, the masses in lb · s
2
/ft (also
referred to as
slugs
), and the accelerations in ft/s
2
[Sec. 12.4].
To solve a problem involving the motion of a particle, Eq. (12.2) should
be replaced by equations containing scalar quantities [Sec. 12.5]. Using
rectangular components
of
F
and
a
, we wrote
o
F
x
5
ma
x
o
F
y
5
ma
y
o
F
z
5
ma
z
(12.8)
Using
tangential and normal components
, we had
©
F
t
5
m
dv
dt
©
F
n
5
m
v
2
r
(12.9
9
)
We also noted [Sec. 12.6] that the equations of motion of a particle
can be replaced by equations similar to the equilibrium equations
used in statics if a vector
2
m
a
of magnitude
ma
but of sense oppo
site to that of the acceleration is added to the forces applied to the
particle; the particle is then said to be in
dynamic equilibrium
. For
the sake of uniformity, however, all the Sample Problems were solved
by using the equations of motion, first with rectangular components
[Sample Probs. 12.1 through 12.4], then with tangential and normal
components [Sample Probs. 12.5 and 12.6].
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 Fall '11
 IB
 Force, Mass, General Relativity, Particle

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